Related papers: Spectral Projections for Density Matrices in Quant…

We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral…

We present a protocol that allows the estimation of any density matrix element for continuous-variable quantum states, without resorting to the complete reconstruction of the full density matrix. The algorithm adaptatively discretizes the…

Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…

In this paper, we propose a spectral framework that embeds 1D and 2D quasiperiodic Helmholtz eigenvalue problems into higher-dimensional (2D and 4D) periodic spaces via the projection method \cite{jiang2014numerical, jiang2024numerical}. To…

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties…

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

In these notes I explain how to describe one-dimensional quantum systems that are simultaneously near to, but not exactly at, a critical point, and in a far-from-equilibrium steady state. This description uses a density matrix on scattering…

The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…

This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn's problem, the…

Using a recently introduced tensor network method, we study the density of states of the lattice Schwinger model, a standard testbench for lattice gauge theory numerical techniques, but also the object of recent experimental quantum…

A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…

Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…

The vacuum state -- or any other state of finite energy -- is not an eigenstate of any smeared (averaged) local quantum field. The outcomes (spectral values) of repeated measurements of that averaged local quantum field are therefore…

We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schr\"odinger…

Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…

A collective description of density matrix is presented for identical multi-level atoms, which are either excited initially, driven coherently or pumped incoherently. The density matrix is defined as expectation value of projection or…

We derive a density matrix (DM) theory for quantum cascade lasers (QCLs) that describes the influence of scattering on coherences through a generalized scattering superoperator. The theory enables quantitative modeling of QCLs, including…

We present a simple, perturbative approach for calculating spectral densities for random matrix ensembles in the thermodynamic limit we call the Perturbative Resolvent Method (PRM). The PRM is based on constructing a linear system of…

In this note we lay some groundwork for the resource theory of thermodynamics in general probabilistic theories (GPTs). We consider theories satisfying a purely convex abstraction of the spectral decomposition of density matrices: that…